Is there a golden board, handed to mankind by god the almighty himself, saying that Siberia is this or that? No, it's just human convention what to call Siberia and what not. Now there seem to be different conventions on this matter. In many European countries it is common to say "Siberia" when you mean "Asian part of Russia". In fact, that's what I was taught in geography classes in school: Siberia = Asian part of Russia, divided into 1) West Siberian Plain, 2) Central Siberian Plateau, and 3) the Far East. A rough disposition, but complemented with the most important rivers, cities etc a handy overview.
Now of course Russians and others are entitled to object that their useage of the terms Siberia and Far East is different, but their view is not more right or wrong than the European one - it's just a different convention, and to accuse people in Finland or elsewhere of ignorance because they use the term Siberia in a different way is unfair and wrong.